Eyani sits next to 4 phonetic neighbors — Ayani, Naomi, and Yani are the closest matches by sound. Most share Eyani's Modern American-origin cluster, so the rhythm and vowel shape carry across the list.
You searched for names like
"modern invented name, possibly beautiful one"
"moon"
Similar sound: These names share phonetic patterns with Eyani — similar vowel sounds, consonant clusters, or rhythm.
Shared roots: Several names on this list have Modern American origins, giving them the same cultural heritage as Eyani.
Rhythm: Eyani is a 3-syllable name. Names with the same syllable count tend to feel interchangeable when you're narrowing your list.